Fenwick tree maintenance intervals and support the addition interval

So that the original array is \ (\ {A_N \} \) , the difference array \ (\ {d_i = a_i-
a_ {i-1} \} \) apparently \ (a_x = \ sum_ {i = 1} ^ xd [i ] \)
we now require \ (\ sum_ {i = 1
} ^ x a_i \) to each \ (a_i \) are represented by the above forms, there \ (\ sum_ {i = 1 } ^ x a_i = \ sum_ {i = 1} ^
x d_i (x-i + 1) = (x + 1) \ sum_ {i = 1} ^ x d_i- \ sum_ {i = 1} ^ x id_i \) then fired 2 Fenwick tree maintenance \ (\ {d_i \} \ ) and \ (\ {id_i \} \ ) to